The analysis of laterally loaded piles is generally carried out by idealizing the soil mass as Winkler springs, which is a crude approximation; however this approach gives reasonable results for many practical applications. For more precise analysis, the three- dimensional finite element analysis (FEA) is one of the best alternatives. The FEA uses the modulus of elasticity $E_s$ of soil, which can be determined in the laboratory by conducting suitable laboratory tests on undisturbed soil samples. Because of the different concepts and idealizations in these two approaches, the results are expected to vary significantly. In order to investigate this fact in detail, three-dimensional finite element analyses were carried out using different combinations of soil and pile characteristics. The FE results related to the pile deflections are compared with the closed-form solutions in which the modulus of subgrade reaction $k_s$ is evaluated using the well-known $k_s-E_s$ relationship. In view of the observed discrepancy between the FE results and the closed-form solutions, an improved relationship between the modulus of subgrade reaction and the elastic constants is proposed, so that the solutions from the closed-form equations and the FEA can be closer to each other.